List of top Mathematics Questions

If x+y+z=a and the maximum value of \(\frac{a}{x}+\frac{a}{y}+\frac{a}{z}\) is 81λ, then the value of λ is:

Let the solution curve $y=y(x)$ of the differential equation $\frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^3-\tan ^{-1} x^3}{\sqrt{\left(1+x^6\right)}}\right\}$ pass through the origin Then $y(1)$ is equal to :
Let a unit vector \( \mathbf{OP} \) make angles \( \alpha, \beta, \gamma \) with the positive directions of the coordinate axes \( OX, OY, OZ \), respectively, where \( \beta \in [0, \frac{\pi}{2}] \), and \( \mathbf{OP} \) is perpendicular to the plane through the points \( (1,2,3) \), \( (2,3,4) \), and \( (1,5,7) \). Then which one of the following is true?
An urn contains 7 green and 5 yellow balls. Two balls are drawn at a time. The probability that both balls are of the same colour is
Let f:(0,1)→R be the function defined as f(x)=[4x](x-\(\frac{1}{4}\))2(x-\(\frac{1}{2}\)), where [x] denotes the greatest integer less than or equal to x .Then which of the following statements is(are) true?
R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.
If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.
Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of
(a) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students
A piece of string is 30 cm long. What will be the length of each side if the string is used to form : 
  1. a square? 
  2.  an equilateral triangle? 
  3.  a regular hexagon?
State the number of lines of symmetry for the following figures: 
  1. An equilateral triangle 
  2.  An isosceles triangle 
  3.  A scalene triangle 
  4.  A square 
  5.  A rectangle 
  6.  A rhombus 
  7.  A parallelogram 
  8.  A quadrilateral 
  9.  A regular hexagon 
  10.  A circle

In Fig. 9.23, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

A,B and C are three points on a circle with centre O

If A=\(\begin{bmatrix}2&-1&1\\-1&2&-1\\1&-1&2\end{bmatrix}\)verify that A3-6A2+9A-4 I=0 and hence find A-1 

Fill in the blanks.
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
(e) ____ – 15 = – 10
Find the area of each of the following triangles:
list of triangles
The total revenue in Rupees received from the sale of \(x\) units of a product is given by \(R(x)=13x^2+26x+15\).The marginal revenue, when \(x=7\) is
Find the multiplicative inverse of the complex number \(√5+3i\)\(\)
A pair of dice is thrown $200$ times. If getting a sum of $9$ is considered a success, then find the mean and the variance respectively of the number of successes.
Find the value of the following expressions, when x =–1: (i) 2x – 7 (ii) – x + 2 (iii) x2+2x+1 (iv) 2x2–x–2
The mean of 50 observations is 36. If two observations 30 and 42 are deleted, then the mean of the remaining observations is
Find the ratio of the following:
(a) 30 minutes to 1.5 hours
(b) 40 cm to 1.5 m
(c) 55 paise to ₹1
(d) 500 mL to 2 litres
A Gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure). [Use \(\pi=\frac{22}{ 7}\)]
A Gulab jamun, contains sugar syrup

In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.

four points on a circle. AC and BD intersect at a point

An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
An umbrella has 8 ribs which are equally spaced
If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:\(\frac{(\text{1 + tan² A})}{(\text{1 + cot² A})} = (\frac{\text{1 - tan A }}{\text{ 1 - cot A}})^²= \text{tan² A}\)